Is it possible for the program itself to continue running while one of its activities has been finished by the system?

Yes, an Android application can continue to operate even if one of its activities has been terminated by the system. Activities are just one component of an application. If the system destroys an activity (for example, due to lack of memory), other components such as services or other activities can continue to run.

For example, if you have a background service running, it will continue to operate regardless of whether the current activity has been destroyed. Also, the application can be in a state where the activity is destroyed, but the application process is still alive, and other components can perform tasks.